The Influence Of Properties Of Subgroups On Coleman Automorphisms Of Finite Groups

Coleman automorphisms begin with the study of the normalize problem for the group in the units group of integral group rings.From the point of view for group theory,this dissertation explores the influence on Coleman automorphisms of finite groups through using the properties of subgroups.Firstly,we study the self-centered normal subgroup of finite groups and proved that all Coleman automorphisms are inner when these finite groups are under some conditions.Secondly,we study the Coleman automorphisms of extensions of a finite nilpotent group by a cyclic group.We give a concrete construction of the Coleman automorphisms of the finite groups.Finally,we work out the Coleman outer automorphism of generalized quaternion group.Coleman automorphisms play a significant role in the study of normalizer problem for integral group rings.